On the same set of axes consider the line y=x+1 and the parabola y2=4x.
a. (i) Construct a table of at least five convenient points for the parabola and three for the line, then draw accurate sketches of both curves for 0≤x≤5.
b. (ii) Solve the simultaneous equations to obtain all point(s) of intersection of the two graphs.
c. (iii) From your algebraic result and the sketch, state whether the line is a tangent to the parabola, a secant that cuts it twice, or does not meet it.
d. (iv) Using the sketch, describe how the relative positions of the two graphs illustrate the difference between a constant rate of change and a variable rate of change.